Modelling and Simulation of Micro-Milling Process

Modelling and Simulation of Micro-Milling Process 1

1

2

1

T. Özel , X. Liu and A. Dhanorker Manufacturing Automation and Research Laboratory, Dept. of Industrial & Systems Engineering Rutgers University, Piscataway, New Jersey, U.S.A. 2

Microlution Inc., Chicago, IL 60612, USA

Abstract Micro-milling is a direct operation to manufacture net-shaped small parts offering alternative to other micromanufacturing processes. It is a flexible method of fabricating three-dimensional (3-D) features including micro molds/dies and fully functional metal devices specifically with recently developed miniature machine tools. Increasing popularity of micro-milling has sparked the interest of researchers to study the micro-milling processes to improve the quality, reliability and productivity. In this paper, experimental and modelling studies on micro-milling of AL 2024-T6 aluminum and AISI 4340 steel are presented. Micro-milling experiments are conducted using 0.635 mm diameter end mill at spindle speeds up to 80,000 rpm. Experimental studies include dynamic force measurements to understand the influence of feed rate and spindle speed on the forces and surfaces generated. The finite element modelling of micro-milling based on large plastic deformations is also conducted to predict chip formation and temperature fields without considering process dynamics. Size effects and minimum chip thickness related to edge radius and chip load on the workpiece deformations are also investigated. Keywords: Micro-milling, Finite Element Modelling, Size Effect, Minimum Chip Thickness

1

INTRODUCTION

The demand for miniaturized meso-(100 µm-10 mm)/ micro-(0.1-100 µm) devices with high aspect ratios and superior surfaces has been rapidly increasing in aerospace, automotive, biomedical, optical, military and micro-electronics packaging industries [1,2,3]. There is a growing need for fast, direct, and mass manufacturing of miniaturized functional products from metals, polymers, composites, and ceramics. Mechanical micromachining, scaled down versions of turning, milling and drilling, as a cluster of micromanufacturing processes is rapidly gaining momentum because of its viability to directly produce miniature 3-D functional parts [4,5,6,7,8]. Among those, micro-milling process is not only fast to fabricate 3-D features but also cost efficient as compared to other micro-manufacturing processes. Parts with 3-D geometry are directly machined one at a time not requiring batch set-up. Micro-milling can achieve good accuracy, low surface roughness, and can provide high material removal rates (MRR) with feature sizes as small as 5-10 µm particularly with recently developed miniature machine tools [9]. The smallest tungsten-carbide micro end mills available on the market are about 25 µm in diameter. Micro end mills with diameter from 23 µm (.0009”) down to 5 µm (.0002”) are also fabricated for special request, and currently being tested only in the research institutions [10]. Such micro end mills are utilized in direct fabrication of micromolds/dies from tool steels for injection molding and micro-forming applications [11,12,13]. Increasing process viability and productivity for micro-milling requires use of high MRR on a variety of materials including metal alloys, polymers and ceramics. However, there are still issues associated with the relative quality of the surfaces generated such as formation of undesired burrs, excessive tool wear and sudden tool failure. Increasing popularity of mechanical micro-machining operations has sparked the interest of researchers to study the micro-milling processes to improve the

productivity and also to understand how they differ from conventional milling processes [14,15,16]. The fundamental difference between micro-milling process and conventional milling processes arises due to scale of the operation, while they are kinematically the same. The main differences between the micro-milling and conventional milling can be summarized as follows. The ratio of feed per tooth to radius of the cutter is much greater in micro-milling than conventional milling, which often leads to an error in predicting cutting forces [14]. The runout of the tool tip even within microns greatly affects the accuracy of the end milling operations at micro scale as opposed to the conventional milling [15]. Micromilling is associated with sudden tool failure due to its highly unpredictable cutting action [16]. The chip formation in the micro-milling depends upon a minimum chip thickness [17] and hence the chip is not always formed whenever tool and workpiece is engaged as opposed to conventional milling [18,19]. The tool deflection in the micro-milling greatly affects the chip formation and accuracy of the desired surface as compared to conventional milling [20]. The tool edge radius (typically between 1- 5 µm) and its uniformity along the cutting edge is highly important as the chip thickness becomes a comparable size to the cutting edge radius [21,22]. Since the chip load is small compared to the cutting edge radius the size effect and ploughing forces become significant on both surface and force generation in micro-milling [23,24]. Micro-milling may result in surface generation with burrs and increased surfaces roughness due to the ploughing-dominated cutting and side flow of the deformed material when the cutting edge becomes worn and blunter [25]. 1.1 Size Effect and Minimum Chip Thickness The difference in mechanics of cutting arises from scaling of the milling operation. The current manufacturing method cannot fabricate end mills mostly out of tungsten carbide in a cobalt matrix (WC-Co) with sharp edges due to limitation of structural strength of the tool at the edge. Widely available micro tools have edge radius ranging 4th International Conference and Exhibition on Design and Production of MACHINES and DIES/MOLDS, Cesme, TURKEY, 21-23/6/2007

from 1 to 5 µm. As the tool diameter decreases, the rigidity of the tool also decreases which leads to tool deflection under heavy chip load and sudden breakage of tool. This limits the chip load, especially in micro-milling, to a few microns per tooth. With the small feed rates the well known size effect, originally discovered in ultra precision diamond cutting [17], becomes prominent in micro-milling. Specific cutting forces depend mostly on the ratio of the uncut chip thickness to the tool edge radius. Due to the highly localized shearing, the specific cutting forces in ultra precision cutting is almost twice that of in conventional cutting.

re t u< re a)

Uncut chip load less than a minimum required

N undeformed chip thickness rotation angle

re

t u >= re

Vf

y x

b) Uncut chip load sufficient to form a chip Figure 2: The minimum chip thickness phenomenon in micro-milling.

feed per tooth

feed rate

chip

Vf

Figure 1: Chip thickness and planar forces during micromilling process. The tool edge radius and small feed/tooth makes the phenomenon of minimum chip thickness very predominant in the micro-milling. A minimum chip thickness is observed where tool engagement with workpiece results in chip formation. In full-immersion micro-milling uncut chip thickness of tu(φ) varies from zero to feed per tooth of fz as shown in Fig.1. Hence the minimum chip thickness for micromilling (tcmin) can be defined as formation of chip when the uncut chip thickness becomes greater than a minimum chip thickness (tu>tcmin) at a certain rotation angle of φ. Unlike precision diamond turning where diamond tools are upsharp with nano-metric edge radius, the minimum chip thickness in micro-milling is greatly affected by the radius of the cutting edge (re) which is usually greater than 1 µm (see Fig.2). The chip is not formed and mostly elastic deformations are induced to the workpiece until tool reaches to a certain rotation angle where a minimum uncut chip thickness develops. A smaller edge radius causes early formation of minimum chip thickness whereas a larger edge radius will result in ploughing of the workpiece. Kim et al. [19] experimentally determined that minimum chip thickness depends upon the ratio of uncut chip thickness to the cutting edge radius which was claimed between 10-25% for the ductile metals. Liu et al. [26] calculated the minimum chip thickness and utilized a ratio (λ=tcmin/re) to describe as function of edge radius. In that study, minimum chip thickness to tool edge radius ratio was found about 35-40% for micro-milling of AL6082-T6 aluminum and 20-30% for AISI 1018 steel at a wide range of cutting speed and edge radius.

2 MICRO-MILLING EXPERIMENTS In this study, micro-milling experiments using flat bottom micro end mils are conducted by taking slot cuts (full immersion) at a constant axial depth of cut and spindle speed for AL2024-T6 aluminum and AISI 4340 steel. The summary of the experimental conditions is given in Table 1. A micro end mill with 0.635 mm tool diameter with 2flutes is used with varying feed per tooth to investigate the effect of feed rate on the cutting forces generated. The microscopic pictures of the tungsten carbide micro end mill are shown in Fig. 3. The cutting forces were acquired using a piezo-electric dynamometer and charge amplifier (Kistler, models 9257B and 5010) with an estimated uncertainty about ±0.2 N. The (x, y, and z) global axis forces have been recorded at 2667, 4000 and 5333 Hz for the spindle speed of 40000, 60000, and 80000 rpm respectively with a PC-based data acquisition system and Kistler DynoWare software. The force signals at each channel of the dynamometer are sampled with twice the tooth passing frequency; hence four samples were collected per rotation.

edge radius (3 µm)

0.635 mm

Figure 3: Two-flute WC-Co micro-end mill. Experimentally measured feed (Fx) and normal forces (Fy) for a constant feed rate of 2.54 µm for three different spindle speeds (40 krpm, 60 krpm, 80 krpm) in micromilling of AL2024-T6 aluminum are given in Fig. 4. Experimentally measured feed and normal forces at

40,000 rpm feed rate at various feed per tooth (1.27 µm, 2.54 µm, 5.08 µm) in micro-end milling of AISI 4340 steel are shown in Fig. 5. Measured forces showed large fluctuations due to process dynamics and continuous shift between ploughing and shearing dominated cutting during micro-milling. There is also the effect of the low sampling rate on the fluctuation of the measured forces. Since there are only four samples collected in one rotation, detailed force generation within a full rotation could not be observed. High bandwidth and high sampling frequency force measurement capability is required for better understanding of the force generation in micro-milling. Feed Force at 2.54 micron and various rpm 4

Feed Force, Fx (N)

3

INFLUENCE OF EDGE RADIUS ON MINIMUM CHIP THICKNESS The influence of edge radius on minimum chip thickness for micro-milling of AL2024-T6 and AISI 4340 steel is investigated by utilizing an analytical model developed by Liu et al. [26]. In their analytical model, workpiece material model and a slip-line field analysis are utilized to estimate the minimum chip thickness for a given tool edge radius, feed rate and surface cutting speed. This analytical model accounts for strain hardening, thermal softening and elastic recovery effects of work material with JohnsonCook constitutive model under high strain, strain-rate and temperate conditions. In the Johnson-Cook model (Eq. 1), the constant A is yield strength of the material at room temperature and ε represents the plastic equivalent

ε&

is normalized with a reference

2

strain. The strain rate

1

strain rate ε&0 . Temperature term in the J-C model

0 -1 40,000 60,000 80,000

-2 -3 0

20

40

60 80 Tool Rotation Angle (Radian)

100

120

Normal Force at 2.54 micron and various rpm 4

40,000 60,000 80,000

3 Normal Force, Fy (N)

3

2 1

reduces the flow stress to zero at the melting temperature of the work material, leaving the constitutive model with no temperature effect.

  ε&    T − Troom   σ = A + B(ε )n 1 + C ln  1 −  &  ε 0    Tmelt − Troom  

[

]

m

  

(1)

Johnson-Cook work material model parameters for AISI 4340 steel and AL 2024-T6 aluminum and thermo mechanical properties for work and tool materials are given in Tables 2 and 3. The tool material is tungsten carbide in a cobalt matrix (WC-Co).

0

4340 Steel

0.36

-1

0.35

-2

0.34 20

40

60 80 Tool Rotation Angle (Radian)

100

120

0.33

Figure 4: Measured feed and normal forces in at 2.54 µm feed per tooth feed rate at various rpm in micro-end milling of AL2024-T6.

0.32 0.31

Normal Force at Various Feed Rates, 40,000 rpm

15

0.3

1.27 micron 2.54 micron 5.08 micron

10

Normal Force, Fy (N)

λn = tcmin/re

-3 0

V = 120 [ m/min ] V = 240 [ m/min ] V = 360 [ m/min ]

0.29

5

0.28 0.5

0

-5

0.37

-10

0.36

1

1.5

2

2.5 3 3.5 Edge Radius [ µ m ] 4340 Steel

4

4.5

5

200 250 300 350 Cutting Speed [ m/min ]

400

450

500

re = 1 [ µ m ] r =3[µm] e r =5[µm] e

-15 0

10

20

30

40

50

0.35

60

Tool Rotation Angle(Radian)

0.34

Feed Force, Fx (N)

0.32

n

30

0.33

m

1.27 micron 2.54 micron 5.08 micron

40

λ = tc in/r

50

e

Feed Force at Various Feed Rates, 40,000 rpm

20

0.31

10 0

0.3

-10

0.29

-20 -30

0.28 50

-40 -50 0

10

20

30

40

50

60

Tool Rotation Angle(Radian)

Figure 5: Measured feed and normal forces at 40,000 rpm feed rate at various feed per tooth in micro-end milling of AISI 4340 steel.

100

150

Figure 6: Predicted minimum chip thickness in micromilling of AISI 4340 steel.

4340 steel, where elastic deformations are smaller. Hence, plastic flow begins at a lower uncut chip thickness. 35

t

25 20 15 10 5

Al 2024−T6

0.45

f = 3.0 [ µ m ] t f = 5.0 [ µ m ] t f = 10.0 [ µ m ]

30

Chip formation angle

For the work material of AISI 4340 steel, the minimum chip thickness to edge radius ratio is estimated to be between 30% and 36% for the range of edge radius (1-5 µm) and the cutting speed (120-360 m/min) as shown in Figure 6. For the work material of AL 2024-T6 aluminum, the minimum chip thickness to edge radius ratio is estimated to be between 42% and 45% for the range of edge radius (1-5 µm) and the cutting speed (120-360 m/min) as shown in Figure 7. A particular cutter rotation angle where the minimum chip thickness is achieved and chip begins to form is denoted as chip formation angle (CFA) as illustrated in Fig.2b. Chip formation angle in relation to the uncut chip thickness, tu (φ ), can be calculated by using the analytical model developed by Liu et al. [26].

0 1

0.445

1.5

2

2.5 3 3.5 Edge radius [ µ m ]

4

4.5

5

Figure 8: Chip formation angle vs. tool edge radius (AISI 4340 Steel).

λn = tcmin/re

0.44

35

0.435

r = 1.0 [ µ m ] e r = 3.0 [ µ m ] e r = 5.0 [ µ m ]

30

e

0.43

0.42 0.5

0.45

0.445

V = 120 [ m/min ] V = 240 [ m/min ] V = 360 [ m/min ] 1

1.5

2

2.5 3 3.5 Edge Radius [ µ m ]

4

4.5

5

Al 2024−T6

Chip formation angle

25 0.425

20 15 10

re = 1 [ µ m ] r =3[µm] e r =5[µm]

5

e

0 2

λn = tcmin/re

0.44

6

8 10 Feed per tooth [ µ m ]

12

14

16

Figure 9: Chip formation angle vs. feed per tooth (AISI 4340 Steel).

0.435

0.43

50 45

0.425

100

150

200 250 300 350 Cutting Speed [ m/min ]

400

450

500

Figure 7: Predicted minimum chip thickness in micromilling of AL 20204-T6 aluminum. Variation of chip formation angle with respect to tool edge radius and workpiece feed rate is computed for micromilling of AISI 4340 steel and AL2024-T6 aluminum as shown in Figures 8 through 11. For micro-milling of AISI 4340 steel and AL2024-T6, Figures 8 and 10 depict the relationship in the plane of CFA/re with three levels of feed per tooth where as Figures 9 and 11 show the relationship in the plane of CFA/ft with three level of edge radius respectively. CFA is found to be larger in micro-milling of AL2024-T6 aluminum compared to micro-milling of AISI 4340 steel. This might be due to higher modulus of elasticity of AISI

Chip formation angle

40 0.42 50

4

f = 3.0 [ µ m ] t f = 5.0 [ µ m ] t f = 10.0 [ µ m ] t

35 30 25 20 15 10 5 0 1

1.5

2

2.5 3 3.5 Edge radius [ µ m ]

4

4.5

Figure 10: Chip formation angle vs. tool edge radius (AL 2024-T6 aluminum).

5

50

r = 1.0 [ µ m ] e r = 3.0 [ µ m ] e r = 5.0 [ µ m ]

45

e

Chip formation angle

40 35 30 25 20 15 10 5 0 2

4

6

8 10 Feed per tooth [ µ m ]

12

14

16

Figure 11: Chip formation angle vs. feed per tooth (AL 2024-T6 aluminum). Figure 13: Finite Element simulation of micro-milling of AISI 4340 steel. 4

Fx (N/mm)

The fully developed continuous chip was simulated at a tool rotation angle of 65° for micro-milling of AL2024-T6 aluminum as shown in Fig. 12. A complete chip formation is observed around 53° of tool rotation angle in micromilling of AISI 4340 steel as shown in Fig. 13 under the aforementioned cutting conditions.

Fy (N/mm)

FINITE ELEMENT SIMULATION OF MICROMILLING Fundamentally, metal cutting process can be considered as a deformation process where deformation is highly concentrated in a small zone. Thus, chip formation in milling process can also be simulated using Finite Element Method (FEM) techniques developed for deformation processes [27]. The main advantage of using such an approach is to be able to predict chip flow, cutting forces, and especially a distribution of tool temperatures and stresses for various cutting conditions. In this section, simulation of the micro-milling process is presented. FEM-based commercially available software, DEFORM-2D, was used for the process simulations. An FEM model is designed as shown in Figs. 12 and 13 for micro-milling of AL2024-T6 aluminum and AISI 4340 steel. Johnson-Cook workpiece material model (Eq.1 and Table 2) is used for rigid-perfectly plastic deformation analysis. Finite Element simulations are conducted for the cutting condition of 80 m/min surface cutting speed and 10 µm feed per tooth using the same micro-end mill geometry as given in Fig.3 with 0.635 mm diameter and 3 µm tool edge radius. In the FEM model, a constant friction factor of 0.65 at the chip-tool-workpiece contacts is used.

5

Figure 12: Finite Element simulation of micro-milling of AL2024-T6 aluminum.

20 35 50 Rotation angle (degrees)

65

80

Figure 14: Predicted forces in micro-milling of AL2024-T6 aluminum.

Fx (N/mm)

a) AL2024 aluminum

b) AISI 4340 steel

Fy (N/mm)

Figure 16: Temperatures (ºC) in the cutting zone during micro-milling.

5

20 35 50 65 Rotation angle (degrees)

a) 10 µm feed per tooth

b) 15 µm feed per tooth

c) 10 µm feed per tooth

d) 15 µm feed per tooth

80

Figure 15: Predicted forces in micro-milling of AISI 4340 steel. Predicted forces are given in Figs. 14 and 15 in FE simulations. Since measured forces indicate large fluctuations, there was no comparison made with the FE simulation results. Predicted temperatures are given in Fig. 16. Temperatures in the cutting zone are predicted around 50-60 °C and around 100-150 °C for micro-milling of AL2024-T6 aluminum and AISI 4340 steel at the same cutting conditions. These temperatures are very low when compared to the temperatures in conventional milling conditions primarily due to the very small chip loads. However, the specific cutting forces are very large when compared to the conventional milling conditions [27]. Typically tool failure is due to temperature-depended accelerated wear rates in high speed milling at conventional scale. In contrast, temperature dependent wear cannot be dominant in micro-milling as evident in predicted temperature distributions in Fig. 16. It is believed that highly fluctuating forces due to a continuous shift between ploughing and shearing dominated cutting modes in micro-milling (see Figs. 4 and 5) are responsible for the sudden tool failure and breakage. High deformation rates are observed in the cutting zone where cutting speed is 80 m/min as shown in Figs. 17a-b. Increasing feed per tooth resulted in slight increases in the temperatures. For example, increase in average temperature was about 15 °C when feed rate was increased from 10 to 15 µm feed per tooth as shown in Figs. 17c-d.

-1

Figure 17: Effective strain rate (sec ) and temperatures (ºC) during micro-milling of AISI 4340 steel. 5 CONCLUSIONS In this paper, experimental and modelling studies on micro-milling of AL 2024-T6 aluminum and AISI 4340 steel are presented. Micro-milling experiments are conducted. Measured forces showed large fluctuations due to process dynamics and continuous shift between ploughing and shearing dominated cutting during micromilling. The minimum chip thickness to edge radius ratio is estimated to be between 42% and 45% for AL2024-T6 aluminum and between 30% and 36% for AISI 4340 steel for the given range of edge radius (1-5 µm) and the surface cutting speed (120-360 m/min). Chip formation angle and its variation with respect to micro-milling conditions are also determined. The finite element modelling of micro-milling based on rigid-plastic deformations is also conducted to predict chip formation, forces, strain, strain-rate and temperature fields without considering process dynamics.

6 REFERENCES [1] Alting, L., Kimura, F., Hansen, H.N. and Bissacco G., 2003, Micro Engineering, Annals of the CIRP, 52/2, 635- 657. [2] De Chiffre, L., Kunzmann, H., Peggs, G.N., Lucca, D. A., 2003, Surfaces in precision engineering, microengineering and nanotechnology, Annals of the CIRP, 52/2, 561-577. [3] Madou, M., 1997, Fundamentals of Microfabrication,” CRC Press. [4] Dornfeld, D., Min, S. and Takeuchi, Y., 2006, Recent advances in mechanical micromachining, Annals of the CIRP, 55/2, 745-768. [5] Masuzawa, T., and Tonshoff, H.K., 1997, Threedimensional micro-machining by machine tools,” Annals of the CIRP, 46/2, 621-628. [6] Friedrich, C.R., Vasile, M.J., 1996, Development of the micro-milling process for high-aspect-ratio microstructures, Journal of Microelectromechanical Systems, 5/1, 33-38. [7] Schaller, T., Bohn, L., Mayer, J., Schubert, K., 1996, Microstructure grooves with a width of less than 50 micrometer cut with ground hard metal micro end mills, Precision Engineering, 23, 229-235. [8] Vasile, M.J., Friedrich, C.R., Kikkeri, B., and McElhannon, R., 1999, Micrometer-scale machining: tool fabrication and initial results, Precision Engineering, 19, 180-186. [9] Vogler, M.P., Liu, X., Kapoor, S.G., Devor, R.E., and Ehmann, K.F., 2002, Development of meso-scale machine tool (mMt) systems, Technical Paper, Society of Manufacturing Engineers, MS02-181. [10] Weule, H., Huntrup, V., Tritschle, H., 2001, Microcutting of steel to meet new requirements in miniaturization, Annals of the CIRP, 50/1, 61-64. [11] Uhlmann, E., and Schauer, K., 2005, Dynamic load and strain analysis for the optimization of micro end mills, Annals of the CIRP, 54/1, 75-78. [12] Schmidt, J., Spath, D., Elsner, J., Huentrup, V. and Tritschler, H., 2002, Requirements of an industrially applicable microcutting process for steel microstructures, Microsystem Technologies, 8, 402-408. [13] Schmidt, J., and Tritschler, H., 2004, Micro cutting of steel, Microsystem Technologies, 10, 167-174. [14] Bao, W.Y., and Tansel, I.N., 2000, Modeling microend-milling operations. Part I: analytical cutting force model, International Journal of Machine Tools and Manufacture, 40, 2155–2173. [15] Bao, W.Y., and Tansel, I.N., 2000, Modeling microend-milling operations. Part II: tool run-out, International Journal of Machine Tools and Manufacture, 40, 2175–2192. [16] Bao, W.Y., and Tansel, I.N., 2000, Modeling microend-milling operations. Part III: influence of tool wear, International Journal of Machine Tools and Manufacture, 40, 2193–2211. [17] Ikawa, N., Shimada, S., and Tanaka, H., 1992, Minimum thickness of cut in micromachining, Nanotechnology, 3(1), 6–9. [18] Kim, C.J., Bono, M., and Ni, J., 2002, Experimental analysis of chip formation in micro-milling,” Transactions of NAMRI/SME, 30, 247-254. [19] Kim, C.J., Mayor, J.R., and Ni, J., 2004, A static model of chip formation in microscale milling,” ASME Journal of Manufacturing Science and Engineering, 126, 710-718.

[20] Dow, T.A., Miller, E.L., and Garrard, K., 2004, Tool force and deflection compensation for small milling tools,” Precision Engineering, 28, 31-45. [21] Lucca, D.A., and Seo, Y.W., 1993, Effect of tool edge geometry on energy dissipation in ultra precison machining,” Annals of the CIRP, 42/1, 8386. [22] Melkote, S.N. and Endres, W.J., 1998, The importance of including the size effect when modeling slot milling,” ASME Journal of Manufacturing Science and Engineering, 120, 6875. [23] Vogler, M.P., DeVor, R.E., and Kapoor, S.G., 2004, On the modeling and analysis of machining performance in micro-endmilling, Part I: Surface generation, ASME Journal of Manufacturing Science and Engineering, 126, 685-694. [24] Vogler, M.P., DeVor, R.E., and Kapoor, S.G., 2004, On the modeling and analysis of machining performance in micro-endmilling, Part II: Cutting force prediction, ASME Journal of Manufacturing Science and Engineering, 126, 695-705. [25] Lee, K., and Dornfeld, D.A., 2002, An experimental study on burr formation in micro milling aluminum and copper, Transactions of NAMRI/SME, XXX, 255-262. [26] Liu, X., DeVor R.E., Kapoor, S.G., 2006, An analytical model for the prediction of minimum chip thickness in micromachining, ASME Journal of Manufacturing Science and Engineering, 128, 474481. [27] Özel, T., and T. Altan, 2000, Process simulation using finite element method- prediction of cutting forces, tool stresses and temperatures in high-speed flat end milling process, International Journal of Machine Tools and Manufacture, 40/5, 713-738.

Material Tool Tool diameter (mm) Axial depth of cut (mm) Spindle speed (rpm) Cutting speed (m/min) Feed per tooth (µm)

AL 2024-T6 aluminum AISI 4340 steel 2- Flute Carbide End Mill 0 with 30 helix angle 0.635 0.127 40000, 60000, 80000 79.8, 119.7, 169.65 1.27, 2.54, 5.08

Table 1: Micro-end milling experiment parameters

Material

A (MPa)

B (MPa)

n

C

m

Tmelt (ºC)

AISI 4340

792.0

510.0

0.26

0.014

1.03

1520

AL 2024-T6

369

684

0.73

0.0083

1.7

502

Table 2: Johnson-Cook material model constants

AISI 4340 3

AL 2024-T6

WC-Co

Density (g/cm )

7.85

2.78

15.7

Modulus of elasticity (GPa)

205

73.1

650

Poisson’s ratio

0.29

0.33

0.25

Specific heat capacity (J/g-ºC)

0.475

0.875

0.26

Thermal conductivity (W/m-K)

44.5

121

28.4

Thermal expansion (µm/m-ºC)

12.3

23.2

5.2

Table 3: Thermo mechanical properties of work and tool materials